Transmissions are provided in motor vehicles in many configurations for providing speed-changing gears between an engine and a drive axle. One such example is a dual dry clutch transmission. In general, a dual dry clutch transmission includes a pair of gearboxes operating in parallel, each with its own clutch and allowing for the selection and engagement of subsequent gears. The dual dry clutch transmission provides engagement of subsequent gears while the prior gear remains engaged. In one configuration, a dual dry clutch transmission includes a dual clutch housing that is supported in a transmission housing by a support bearing. During use, the dual clutch housing can operate at high revolutions per minute. Moreover, as the dual clutches operate in a dry or oil-less environment, the surrounding temperatures tend to increase. In some operating scenarios it is potentially challenging to sufficiently cool the support bearing. Thus, while these dual clutch transmissions work for their intended purpose, there is a need for improvement in the relevant art.